ELEMENTARY METHODS FOR THE ANALYSIS OF DICHOTOMOUS OUTCOMES IN UNSELECTED SAMPLES OF TWINS

This paper presents an elementary statistical method for analyzing dichotomous outcomes in unselected samples of twin pairs using stratified estimators of the odds ratio. The methodology begins by first randomly designating one member of each twin pair as an "index" twin and the other member as the "co-twin." Stratifying on zygosity, odds ratios are used to measure the association between disease in the index twin and disease in the co-twin. From these zygosity-specific tables we calculate the Woolf-Haldane estimator of the common odds ratio (psi(F), the weighted average of the zygosity-specific odds ratios), the Mantel-Haenszel test statistic (chi(M-H)2) for the common odds ratio, and a test (chi(G)2) for the difference in the zygosity-specific odds ratios. In this application, psi(F) provides an estimate of the familial association for disease and the accompanying chi(M-H)2 provides a test of the null hypothesis, psi(F) = 1 (i.e., there is no evidence for a familial influence on disease). The chi(G)2 is a test of the null hypothesis that psi(MZ) = psi(DZ); a significant value for chi(G)2 suggests a genetic influence on disease (assuming that the observed odds ratios follow a pattern where psi(MZ)>psi(DZ)). A new test statistic (chi(c)2) is proposed that incorporates the expectation that psi(MZ) = psi(DZ) under a purely additive genetic model with no common environmental effects. A significant value of chi(c)2 indicates that the different odds ratios across zygosity are partly due to common environmental influences. Conversely, a nonsignificant value of chi(c)2 is an indication that the zygosity-specific odds ratios are due solely to additive genetic effects and not to common environment. This basic approach is extended to examine the effects of measured indicators of the specific environment and the assessment of certain forms of gene by environment interaction. All of the methods are easily understood, highly flexible, readily computed using a hand calculator, and incorporate the inherent genetic information contained within twin samples.